Story time! Robert Axelrod

Contest #1 Call for entries to game theorists All entrants told of preliminary experiments 15 strategies = 14 entries + 1 RANDOM Round-robin tournament against all other players and “twin” Each game: 200 iterations 3 CD D C

And, the winner is… TIT FOR TAT “Cooperate on first move, thereafter reciprocate opponent’s previous action” Shortest program submitted By psychologist, Anatol Rapoport

What’s wrong with TIT FOR TAT? Not subgame perfect! One-period Nash reversion, however, is subgame perfect.

Analysis: “Nice” Guys Finish First Top 8 strategies never defect first.

Analysis: To Forgive, Divine Top two rules are willing to cooperate even after defections, if other player is “contrite” DOWNING - “Kingmaker” - Tries to learn behavior of other player; starts by defecting twice. - Hurts strategies that are unforgiving.

Other Interesting Strategies TIT FOR TWO TATS –Retaliate only if previous two are D’s –Would have won tournament, if entered NICE DOWNING –Like DOWNING, but start with C’s –Would have won tournament, if entered

Contest #2 Same set up as Contest #1, except… Entries from first-round contestants as well as open call in magazine 63 strategies = 62 entries + 1 RANDOM Each game iterated an uncertain number of times, with probability of ending

And, the winner is… TIT FOR TAT, again! (Again, by Anatol Rapoport)

Analysis: Contest #1 Lessons Validated 14 of top 15 strategies never defect first. 14 of bottom 15 strategies were not “nice”. Forgiveness important.

Analysis: Be Retaliatory Some entrees tried to take advantage of “nice” strategies: TRANQUILIZER – cooperate first, if other cooperates, too, throw in a few defections. TESTER – defect first, if other doesn’t retaliate, cooperate twice, then alternate defection and cooperation. If other ever defects, do TIT FOR TAT. TIT FOR TWO TATS and NICE DOWNING were both submitted in contest #2, and both got clobbered by TRANQUILIZER and TESTER.

Analysis: Sneaki- ness Doesn’t Pay Entrees that try to take advantage of “nice” strategies don’t gain as much as they lose. TRANQUILIZER – 27 th place in tournament. TESTER – 46 th place in tournament (out of 63).

Robustness of TIT FOR TAT In six variations of Contest #2, TIT FOR TAT took first place in five and second place in one. In a population simulation with 63 strategies (right), TIT FOR TAT emerges as the winner. In an genetic algorithm experiment (1987), TIT- FOR-TAT-like algorithms prevailed.

General Lessons Don’t be envious. (It doesn’t matter if others win.) TIT FOR TAT never scores more than the other player. Be nice. (Don’t defect first.) The best way to do well is to cooperate with others who are also nice. Retaliate swiftly. Or else others will take advantage. Forgive. Feuds are costly. Defections shouldn’t prevent cooperation later on. Don’t be too clever. Too much cleverness looks RANDOM.

CooperateShoot to Kill Cooperate Payoff Matrix You Them Both live. Trench Warfare as repeated PD You live and hurt other side. You die and they win. Both die. For a single round, no matter what the enemy does, it’s better to shoot to kill. But for an indefinite number of rounds…?

Cooperation spontaneously evolved: “If the British shelled the Germans, the Germans replied, and the damage was equal.” “[A British staff officer was] astonished to observe German soldiers walking about within rifle range…” “These people … did not know there was a war on. Both sides … believed in … ‘live and let live’.” “Suddenly a salvo arrived but did no damage. Naturally both sides got down and our men started swearing at the Germans, when all at once a brave German got on to his parapet and shouted out ‘We are very sorry about that; we hope no one was hurt. It is not our fault, it is that damned Prussian artillery.’” Trench Warfare in WWI